|  UNIVERSITY  OF  CALIFORNIA 

ANDREW 

SMITH 

HALLID1& 


REGEHT 


,._..-., 

19O1 


PROF.  WARE'S 

• 

$1O7OOO 

PRIZE    HTJLE 


! 


uw  of 


Two-thirds  of  the  time  and  labor  saved  —  requiring  only 
one  division  in  debit  and  credit  accounts. 

TO  WHICH  IS  APPENDED 

RANKIN'S  PERPETUAL  ALMANAC. 


PHILADELPHIA  : 

CLAXTON,  REMSEN  &  HAFFELFINGER, 

624,  626  &  628  MARKET  STREET. 

1877. 


Entered,  according  to  Act  of  Congress,  in  the  year  1872,  by 
I  PROP.  W.  POWELL  WARE,  in  the  Office  of  the  Librarian 

of  Congress,  at  Washington,  D.  C. 


103997 


INDEX. 


PAGE 

Author's  Preface,. 5 

General  Rules  of  Equation, 7 

Dr.  and  Cr.  Accounts, 9 

Bills  on  Unequal  Time, 14 

Bills  on  Equal  Time,. .  / 16 

Monthly  Statements, 18 

Balance  Falling  Due  prior  to  First  Transaction, — 19 

Computation  of  Interest  for  360  Days  per  Annum,. 20 

365      "         "         ....21 

Interest  by  Cancellation, 22 

To  Calculate  Interest  for  Days, 24 

Computing  Percentage, 25 

Multiplication, 27 

Diamond  or  Chain  Rule, 29 

Multiplication  of  Fractions, 31 

Division  of  Fractions, 32 

Guide  in  Addition 33 

Conversion  of  Sterling  Money, 34 

Barter, 35 

Discount, 36 

Wood  Measure,  &c 37 

Names  of  Coins, 39 

Value  of  Foreign  Money, 40 

Magic  Square, 45 

Prof.  Ware's  Challenge, 46 

Decision  of  the  Judges, .47 


PREFACE. 


In  presenting  to  the  public  his  system  of 
averaging  accounts,  the  author  claims  as  new 
his  method  of  arranging  the  time  and  the 
computation  of  the  interest.  The  time  can 
be  almost  instantly  arranged,  without  liability 
to  error,  thereby  showing  the  number  of 
months  and  days  for  which  the  interest  must 
be  obtained  on  each  bill.  The  rate  per  cent, 
used  calculating  the  interest  is  such  as  to 
enable  accountants  to  make  their  own  calcu- 
lations faster,  and  with  less  liability  to  error, 
than  it  could  be  taken  from  an  interest  table, 
— thereby  rendering  them  perfectly  inde- 
pendent of  tables, — by  which  they  can  become 
walking  libraries,  and  not  portable  machines, 
as  I  have  found  to  be  the  case  with  a  great 
number  of  accountants  from  personal  obser- 
vation. Among  the  many  multifarious  and  I 
distracting  duties  of  the  counting-room  none 
are  so  tedious  and  perplexing,  and  are  the 
cause  of  so  many  misunderstandings  and 
disputes,  as  that  of  AVERAGING  ACCOUNTS. 

The  question  naturally  arises,  why  is  this  ? 
I  answer,  because  most  of  the  systems  now  in 
use,  are  long,  unwieldily,  often  inaccurate, 
and  therefore  not  reliable.  I  would  especially 


PROP.  WARE'S  SYSTEM  OP 


call  the  attention  of  accountants  to  the  im- 
mense loss  of^w^and  labor  in  averaging  debit 
and  credit  accounts  by  the  ordinary  methods, 
which  require  the  extension  of  all  time-bills 
to  their  maturities,  the  re-arrangement  of  the 
account,  the  getting  of  the  number  of  days 
from  one  date  to  the  other,  (with  numerous 
multiplications,  and  liability  to  error),  the 
averaging  of  the  debit  side  first,  the  credit  side 
next,  and  then  the  balance ;  performing  a  vast 
amount  of  labor;  making  three  divisions  to 
find  out  one  thing,  viz:  When  the  balance  of 
the  accounts  is  due. 

What  is  the  fact  to  be  determined  about  a 
debit  and  credit  account  ?  Simply  to  ascertain 
when  the  balance  is  due.  Why  not  go  to  work, 
do  that  and  nothing  more.  By  the  following 
RULE  accountants  can  take  the  most  com- 
plicated accounts  ever  spread  on  a  ledger, 
just  as  they  stand,  arranging  the  time  with 
a  pencil  on  the  margin,  taking  a  small  slip  of 
paper,  writing  down  the  interest  as  fast  as 
they  can  make  the  figures,  average  the  bal- 
ance direct  by  one  division  only,  thereby 
saying  two-thirds  of  their  time  and  labor,  with 
one-tenth  of  the  liability  to  error.  To  the  expe- 
rienced and  critical  accountant  this  may  seem 
presumptuous ;  but  for  the  truth  of  the  above 
assertion,  he,  and  all  others  interested,  are 
respectfully  referred  to  the  following  pages,  by 

THE  AUTHOR 


EQUATION   OF   PAYMENTS. 


GENERAL   RULES 


Start  at  the  first  of  the  month  in  which  the 
first  transaction  takes  place,  instead  of  the 
date  of  the  first  bill.  Call  the  first  month  0, 
then  number  the  following  months  in  their 
regular  order,  setting  the  number  in  the  mar- 
gin, or  elsewhere. 

Each  bill  then  shows  at  sight  the  time  for 
which  the  interest  must  be  obtained. 

NOTE. — Compute  interest  at  1  per  cent,  per 
month.  Any  amount  of  dollars  shows  its  own 
interest  (in  cents)  for  one  month.  Point  off 
the  right  hand  figure,  and  the  interest  is  shown 
(in  cents)  for  one-tenth  of  a  month  (or  3 
days). 


PROF.  WARE'S  SYSTEM  OF 


BULK 

Multiply  the  whole  amount  of  dollars  by  the 
number  of  months  required.  Multiply  one- 
tenth  of  the  dollars  by  one-third  the  number 
of  days  required,*  setting  the  products  under 
each  other  until  all  the  interest  is  obtained ; 
add  up  the  interest,  annex  two  ciphers  to  the 
right,  and  divide  by  the  footing  of  the  bills 
(in  dollars  only) ;  the  answer  will  be  in  months 
and  hundredths  of  months.  Multiply  the 
hundredths  by  30  to  bring  it  into  days. 

N.  B, — Add  the  month  in  the  margin  to 
those  in  the  face  of  the  bills  in  all  cases  of 
unequal  time. 

*NoTE. — One-third  of  any  number  of  days 
shows  how  many  tenths  are  contained  therein. 

EXAMPLE. 

24  days  contain  8  tenths,  25  days  8£  tenths, 
26  days  Sf  tenths,  27  days  9  tenths,  &c. 


EQUATION   OF   PAYMENTS. 


DEBIT  AND  CEEDIT  ACCOUNTS 

OF  ALL  CLASSES, 
(To  find  when  tJie  balance  is  due,) 

EULE. 

Arrange  the  time,  commencing  at  the  first 
of  the  month  on  which  the  first  transaction 
took  place,  whether  debit  or  credit.  Then 
compute  the  interest  on  both  sides  of  the  ac- 
count for  the  time  called  for  in  each  bill; 
subtract  the  smaller  amount  of  interest  from 
the  larger,  annex  two  ciphers  to  the  right  of 
the  difference  in  interest  (read  so  many  cents), 
and  divide  by  the  'balance  of  the  account.  As 
many  months  and  days  as  are  obtained  in  the 
quotient,  or  answer,  so  long  will  the  balance 
be  falling  due,  from  the  cipher  or  starting 
point. 


10  PROF.  WARE'S  SYSTEM  OF 

EXAMPLE. 
Dr. 

1871.  0,  July  27,  Mds.  4  mos 1350  |    ^'^ 

4,  Nov.  12,    "      6    "    2531J210.12 

i  01  Q    40 

1872.  6,  Jan.  18,    "      5     "    194°  f    11.64 

9  Apr.  21,  Cash 1170  j- 10^ 


$6991  $667.90 
Cr. 

1871.  l,Aug.    9,  Cash 750  j-     ^'^ 

3,  Oct.     5 ,*Dft.  90  days 961  |   5J  ^ 

1872.  9,  Apr.     6,  Cash 850  j-    7j  ^ 

13,  Aug.  15,  Note  60  days 500  I   7^ '  ^ 


$3061  $224.71 


DR.  Int 667.90 

CR.    Int 224.71 


Balance. .  ..3930)44319.00(11.27 

30 

8.10 
lira.  Sd.  from  July  1st. 

Balance  due  June  8,  1872. 


5  days  If  tenths,  or  |  of  961. 


EQUATION   OF   PAYMENTS.  11 

Commence  July  0.  From  July  1st  to  No- 
vember 1st,  is  4  months ;  to  January,  6  months ; 
to  April,  9  months.  From  July  to  August,  1 
month;  to  October,  3  months;  to  April,  9 
months;  to  August  next  year,  13  months. 

Kead  the  bills: — 1st,  you  want  the  interest 
for  4  months  and  27  days ;  2d,  10  months  and 
12  days;  3d,  11  months  and  18  days;  4th,  9 
and  21  days;  5th,  1  month  and  9  days;  6th, 
6  months  and  5  days ;  7th,  9  months  and  6 
days;  8th,  15  months  and  15  days. 

Now  obtain  the  interest : — 

1  month,  at  1  per  cent,  per  month,  is  $13.50  ; 
4  months  is  four  times  as  much,  $54.00 ;  one- 
tenth  of  a  month  is  one-tenth  of  $13.50,  which 
is  $1.35;  27  days  being  nine-tenths,  is  nine 
times  $1.35,  which  is  $12.15;  10  months  is 
ten  times  $25.31,  which  is  $253.10 ;  12  days  is 
four  times  $2.53=$  10.12;  and  so  on  through 
the  whole  account. 

Add  up  the  interest  of  the  Dr.,  then  the  Or.; 
subtract  the  smaller  from  the  larger  amount, 
bringing  down  the  difference,  omitting  the 
point  between  the  dollars  and  cents ;  place  a 
point  to  the  right  of  whole  amount,  then  add 
two  ciphers  to  the  right  of  the  point,  and  di- 


12  PROF.  WARE'S  SYSTEM  OF 


yide  the  difference  of  interest  by  the  balance 
of  the  account.  As  often  as  the  divisor  is 
contained  in  the  dividend,  up  to  the  point,  so 
many  months  you  get;  add  one  cipher  and 
divide,  that  will  give  you  tenths  of  months ; 
add  the  other  cipher  and  divide,  that  will 
give  you  hundredths  of  months.  Your  an- 
swer will  read  11  months  and  27  hundredths 
of  a  month.  Multiply  the  hundredths  by  30, 
which  will  bring  the  time  into  days,  27x30 
=8  days  and  ten  one-hundredths,  which  is 
never  counted  unless  fifty  one-hundredths  or 
upward.  Thus  the  answer  is  11  months  and 
8  days  from  July  1  (inclusive),  1871,  balance 
due  June  8,  1872. 

N.  B. — Xow  comes  in  the  regular  rate  per 
cent.  Any  number  of  days  that  the  balance 
is  paid  before  the  8th  of  June,  the  interest  is 
taken  off  at  the  legal  rate.  Any  number  of 
days  after  the  8th  of  June  the  interest  is  added 
at  the  legal  rate. 


EQUATION  OF   PAYMENTS.  13 

EXAMPLE. 

Dr. 
1872.    0,  Jan.    9,  Mds.  0  mos  ........  181  .  75*    10' 


0,  ll   21,   "  "  "  ........  250.25  -i  ^'SS 

(  i  .  /  o 

2,  Mar.  1,   "  "  «  ........  380.50  •!  3°'f5 

(   .  lo 

2,  "   24,  "  "  "  ........  150.10  J^'.JQ 

(27^00 

3,  Apr.  22,   "  "  "  ........  300.00  *  2.10 

.10 


$1262.60  $101.22 
Cr. 

1872.    l,Feb.    6,  Cash 150|1.30 

2,  Mar.  16,  30  days 200  I  J*^ 

2,    "     27,60    "    200]l'80 

$550  $18.67 


Bal.    $71260 

DR.  Int 101.22 

CR.  Int 18.67 

713)8255.00(11.57 
30 

17.10 
llw.  VHd.from  Jan.  1st. 

Balance  due  Dec.  17,  1872. 


*  Bills  containing  Dollars  and  Cents,  the  cents  are  omitted    | 
if  under  fifty;  and  counted  as  one  dollar  if  fifty  or  upward. 


14  PROF.  WARE'S  SYSTEM  OF 


BILLS  BOUGHT  Off  UNEQUAL  TIME, 
(without  credit.} 

RULE. 

Compute  the  interest  on  each  bill  for  the 
time  called  for  in  the  several  bills  ;  add  up  the 
interest ;  annex  two  ciphers  to  the  right  of  the 
whole  amount,  and  divide  by  the  footing  of 
the  bills,  (the  dollars  only).  The  number  of 
months  and  days  obtained  in  the  quotient, 
will  show  how  long  the  amount  will  be  in 
falling  due  from  the  0,  or  starting  point. 

EXAMPLE. 
Dr. 

1871 .  0,  May    6,  Mds.  3  mos $931  \  27  • 

(       1  .  OO 

0,  -  13,  "  2  «  860|13.'44 

(  '.29 

2,  July  9,  "  4  ••  432  j  25. 92 

)  1.29 

4,  Sept.    1,       "    5    "     384J34.56 

1872.  8,  Jan.  27,       "    Cash 321(25.68 

\    2.88 


$2928   141.18 
2928)14118.00(4.82 
11712  30 


24060     24.60 
23424 

6360    4  mos.  25  d.from  May  1. 
Due  Sept.  25,  1871. 


EQUATION   OF    PAYMENTS.  15 

Commence  May  0 — July,  2  months;  Sep- 
tember, 4  months ;  January,  8  months. 

Read  the  bills — 1st  bill,  3  months,  6  days; 
2d  bill,  2  months,  13  days ;  3d  bill,  2  and  4  are 
6  months,  9  days ;  4th  bill,  4  and  5  are  9 
months,  1  day;  5th  bill,  8  months,  27  days. 

Compute  the  interest — 3  months  is  3  times 
$9.31=427.93;  6  days  is  twice  93c.=81.8G  ;  2 
months  is  twice  $8.60=117.20;  13  days  is  4^ 
times  86c.,  &c.,  &c. 

N.  B. — Multiply  the  whole  amount  of  dollars 
by  the  number  of  months;  one-tenth  the 
dollars  by  one- third  the  days. 


10  PROF.  WARE'S  SYSTEM  OF 

I 


BILLS  BOUGHT  ON  EQUAL  TIME, 

EULE. 

Compute  the  interest  for  the  time  that  each 
bill  calls  for,  up  to  the  date  of  purchase.  Add 
up  the  interest,  annex  two  ciphers,  and  divide 
by  the  footing  of  the  bills  (the  dollars  only) . 

The  months  and  days  obtained  in  the  quo- 
tient will  show  the  average  date  of  purchase, 
from  the  0. 

Add  the  time  of  credit  (whatever  it  may  be) 
to  the  average  date,  and  that  will  show  the 
date  of  maturity. 

N.  B. — The  answer  always  comes  in  months 
and  hundredths  of  months.  Multiply  the 
Jiundredths  by  30,  which  will  give  the  number 
of  days. 


EQUATION   OF   PAYMENTS.  17 

EXAMPLE. 

Dr. 

1871.     0  Feb.     9,     6  mos $430^1    i-20 

(    7 . 68 

2  Apr.  13,    "     "     384 H 


(  7.G8 
•I  1.52 
(  .13 


5  July    6,     "    "     230  J11-50 

(      .46 

5  July'21,     "    "     "M    S'ftj 

7Sept.    2,     "    "     431J30'.17 

(      .28 


$1856    74.74 


1856)7474.00(4.02 
30 


.60    4m.  Id.fromFtb.  1st. 
Average  date,  June  1st — due  6  mos. 

Eead — 1st  bill,  9  days;  2d  bill,  2  months, 
13  days  ;  3d  bill,  5  months,  6  days ;  4th  bill,  5 
months,  21  days;  5th  bill,  7  months,  2  days. 

Compute  the  interest — 9  days  is  3  times 
43c.;  2  months  is  twice  $3.84;  13  days  is  4£ 
times  38c.;  5  months  is  5  times  $2.30 ;  6  days 
is  twice  23 ;  5  months  is  5  times  $3.81 ;  21 
days  is  7  times  38c.;  7  months  is  7  times  $4.31 ; 
2  days  is  f  of  43. 


18  PROF.  WARE'S  SYSTEM  OF 

MONTHLY   STATEMENTS. 
RULE. 

Compute  the  interest  on  each  bill  for  the 
number  of  days  that  each  bill  calls  for. 

Add  up  the  interest,  annex  two  ciphers,  and 
divide  by  the  footing  of  the  bills. 

N.  B.  —  In  a  monthly  statement  the  answer 
will  always  be  in  hundredths  of  months. 

EXAMPLE. 
1871.     Jan.     9,  .........................  187-|     .54 

«      m  pQ-i     2.04 

10,  .........................  681  •{      O 


12,   ........................  438-j  1.75 

18,  .........................  217«  1.80 


Q11  J  *'      ' 

3111     .10 


24,  .........................  221-!  1.76 

27,     ......................  407^  3.66 

30,  ........................  386-1  8.86 


4078  28.57 
4078)2857.  00(.  70 
30 

21.00    21  days. 
Due  January  21. 

Compute  the  interest  for  9  days,  10  days, 
11  days,  &c.  9  days  is  3  times  18c.  ;  10  days 
is  3^  times  68c.;  11  days  is  3f  times  23c.;  12 
days  is  4  times  43c.,  &c. 


EQUATION   OF   PAYMENTS.  19 


Balance  Palling  Due  Prior  to  the  Pirst  Transaction, 

EXAMPLE. 
]ST.  B.  —  Work  as  before. 

Dr. 
1370.     0,  July    4,     Mils  ...............  $3750  j    ^ 

o,   "    21,     "    ..............  2000^  uiob 

0,    "     27,        "     ..............  1850^  10.65 

2,Sept.  3,        ••     ...  ...........   I***  )21.'^ 

2'50 


3,  Oct.  16,        "     ..............     90024' 


1870.       4,  Nov.  24,  Cash, $500  j    2^ 

5,  Dec.     1,  Dft.  30  days, 850  j    51 '  ° 


28 


8,  Mar.     6,  Cash,  .............  60°  j    4?  20 

10,  May     1,  Note  90  days,  ......  800  j  104'^ 


$2750    228.75 


Bal $6970 

228 . 75 — greater  interest. 
93 . 07 — smaller  interest. 


6970)13568.00(1.94 
6970  30 


65980     28.20—1  m.  28d.  back  of  July  1. 
62730 


32500  Balance  due  May  2d,  1870. 


$9720    93.07 
Cr. 


20  PROF.  WARE'S,  SYSTEM  OF 

If  the  interest  of  the  smaller  side  of  the  ac- 
count exceeds  that  of  the  larger  side,  the  time 
counts  back  from  the  starting  point.  In  the 
above  example,  the  smaller  exceeds  the  larger 
by  $135.68,  throwing  the  balance,  1  month 
and  28  days,  back  of  July  1st. 

K.  B. — The  interest  must  be  paid  from  May 
2d  up  to  the  day  of  settlement,  at  the  legal 
rate. 


COMPUTATION,.  OF  INTEREST. 

(For  360  days  per  annum.} 
KULE. 

First  obtain  the  interest  at  12  per  cent,  per 
annum  for  the  required  time ;  then  divide  the 
product  by  12,  which  will  give  the  interest  at 
.1  per  cent,  per  annum.  Multiply  this  quo- 
tient by  the  rate  per  cent,  required.  The  re- 
sult will  be  the  answer  in  cents. 

EXAMPLE. 

What  is  the  interest  on  $1850  for  7  months 
and  27  days,  at  0  per  cent,  per  annum. 


EQUATION   OF   PAYMENTS.  21 

SOLUTION. 

$1850  7  mos.,  27  days,  at  9  per  cent. 

12950 
1665 

12)146.15 

12.18 
9 


$109  62— Ans. 

One  month  is  118.50  ;  7  months  is  7  times 
as  much;  one-tenth  is  $1.85;  27  days  (being 
nine-tenths)  is  nine  times  as  much. 

Add  up  and  divide  the  product  by  12,  which 
is  $12.18,  at  1  per  cent,  per  annum ;  9  per 
cent,  is  0  times  $12.18;  8  per  cent,  would  be 
8  times  $12.18 ;  5  per  cent.,  5  times,  &c.,  &c. 


COMPUTATION  OF  INTEREST. 

(For  065  days  per  annum.} 

RULE. 

Multiply  the  principal  by  the  number  of 
days ;  then  add  one  one-tenth  of  the  product 
to  itself;  then  add  one-half  of  the  one-tenth; 
add  up  the  whole  amount.  If  7  per  cent,  is 
required,  divide  the  product  by  6.  If  6  per 
cent,  is  required,  divide  by  7. 
1  Point  one  for  mills. 


PROF.  WARE'S  SYSTEM  OF 


EXAMPLE. 

What  is  the  interest  on  $875  for  120  days, 
at  7  per  cent,  per  annum  (of  365  days)  ? 

SOLUTION. 
$875    120  days  at  7  per  cent. 


105000 

10500—1  tenth. 
5250— i  of  1  tenth. 


6)120750 


&20.12.5— Ans. 


FOB  COMPUTING-  INTEREST 

BY   CANCELLATION. 


EXAMPLE. 

What  is  the  interest  on  $180  for  2  years,  •' 
months,  and  18  days,  at  8  per  cent,  per  annum. 

SOLUTION, 

100  Principal,  60 
316  time. 

120 
$  per  cent.  2 

s.— I37.92.Q 


EQUATION   OF   PAYMENTS.  23 

1st. — Draw  a  perpendicular  line,  place  the 
principal  on  the  right,  bring  the  years  and 
months,  to  months,  take  J  of  the  days  and 
place  to  the  right  of  the  months,  setting  the 
time  under  the  principal,  and  the  rate  per 
cent,  (whatever  it  may  be)  under  the  time ;  on 
the  left  (in  all  cases)  place  3  and  4.* 

2d.— Divide  with  the  numbers  on  the  left, 
through  any  number  on  the  right  which  they 
will  divide  without  a  remainder,  cancelling 
each  number  as  you  use  them ;  then  multiply 
all  the  un canceled  numbers  together  on  the 
right,  and  divide  (if  any)  by  those  on  the  left. 
The  answer  will  come  in  mills,  if  days  be  in 
the  time ;  if  no  days,  in  cents. 

3d.— If  there  be  one  over  in  taking  the  -J  of 
the  days,  place  a  3  to  the  right  of  a  decimal 
point;  thus  2  years,  7  months,  19  days,  equal 
316.3;  if  two,  place  a  6;  thus  1  year,  5  months, 
20  days,  equal  176.0 — working  as  a  whole 
number  until  done.  Cut  off  in  your  answer 
one  figure  for  each  figure  to  the  right  of  a 
decimal  point  or  points. 

4th. — For  days  only,  place  the  principal,  whole  number  of 
days,  and  the  rate  per  cent,  on  the  ri^ht,  placing  3,  3  and  4  on 
the  f  left,  working  by  rule  2d ;  the  answer  will  be  in  mills. 

*  The  3  and  4  stand  for  the  12  months  in  the  year. 
t  The  3,  3  and  4  stand  for  360  days  in  the  year. 


24  PROF.  WARE'S  SYSTEM  OF 

EXAMPLE  FOR  DAYS. 

What  is  the  interest  on  $720  for  3G  days  at 
9  per  cent,  per  annum. 


720 
H 


Ans. — $6.48.0 


If  the  numbers  will  not  divide,  multiply  all 
the  right  hand  side  together,  and  divide  by  the 
left  multiplied  together,  the  quotient  will  be 
the  answer. 

If  fractional  rates  per  cent,  occur,  bring  it 
to  an  improper  fraction,  placing  the  numerator 
on  the  right,  the  denominator  on  the  left, 
working  as  before. 


SHOET  METHOD  TO  CALCULATE  INTLEEST, 
EULE. 

Multiply  the  principal  by  half  the  number 
of  days ;  that  product  divided  by  30  will  give 
the  answer  in  cents. 


EQUATION    OF   PAYMENTS.  25 

EXAMPLE. 

What  is  the  interest  on  $165  for  16  days,  at 
6  per  cent.  ? 

165  dollars. 

8  half  the  number  of  days. 
3.0)132.0 

.  44  cents. 

Divisors  for  Different  Eates  Per  Cent, 
Any  amount  multiplied  by  the  time  in  days, 
as  per  example:  $200  for  19  days,  and  divide 
by  72,  will  give  you  the  interest  at  5  per  cent, 
per  annum. 

Ans.  $.52.7. 

At  G  per  cent.,  as  above,  divide  by  CO 
"    7  per  cent.,    "      "  "        "    52 

"     8  per  cent.,    "      "  "        "    45 

"    9  per  cent,    "      "  "        "    40 

"  10  per  cent.,    "      "  "        "    36 

"  12  per  cent,    "      "  "        "    30 

"  15  per  cent,    "      "  "        "    24 

"  20  per  cent,    "      "  '«        '4    18 

"  24  per  cent,    •«      «•  "        <l    -15 

"  40  per  cent,    "      "  "        l<    09 


COMPUTING-  PERCENTAGE. 

To  ascertain  what  is  gained  or  lost  b^  selling 
an  ARTICLE  for  which  a  specified  sum  has  been 
paid. 


26  PROF.  WARE'S  SYSTEM  OF 

RULE. — Annex  two  ciphers  to  the  SELLING 
PRICE,  divide  by  the  COST.  The  difference 
between  the  quotient  and  100  will  be  the 
gain  or  loss  per  cent. 

EXAMPLE. — Paid  5  dollars  for  a  BOOK,  and 
sold  it  for  8  dollars.  "What  per  cent,  did  I  gain  ? 

OPERATION—  5)800 

1 .  GO    Ans. — 60  per  cent. 

EXAMPLE. — Paid  10  dollars  for  a  hat,  and 
sold  i  t  f or  8  dollars.  W h  at  per  cen  t.  did  I  lose  ? 

j     OPERATION—  10)800 

80 
Ans  —100  less  80=20  per  cent. 

To  ascertain  what  an  article  should  be  sold 
for,  which  cost  a  specified  sum,  so  as  to  gain 
a  proposed  per  cent. 

RULE. — Multiply  the  COST  by  100,  with  the 
per  cent,  added ;  cut  off  two  figures  to  the 
right.  The  figures  at  the  left  will  show  the 
PRICE  for  which  the  article  must  be  sold. 

EXAMPLE. — Paid  30  cents  per  yard  for 
CLOTH  ;  for  how  much  must  I  sell  it  so  as  to 
realize  20  per  cent,  profit? 

OPERATION —  30 — cost. 

120—100  per  cent  added. 

36.00    I  must  sell  it  for  36  cents. 


EQUATION    OF   PAYMENTS.  27 


MULTIPLICATION. 


EXAMPLES. 

In  multiplying,  it  is  easier  to  multiply  by 
2,  3,  4,  and  5,  than  by  7,  8,  or  9,  &c. 

I  shall  now  present  examples  in  Multipli- 
cation. 

1.  Multiply  428  by  15. 

428x15  ^   l^ace   ^1C  -^  a^   ^1C 

2140  right  of  428,  and  use  the  sign 

of  Multiplication  ;    but  this 

6420  is   not   necessary,  from   the 

fact  that  it  may  be  placed  anywhere  or   not 

written  at  all ;  this  of  course  is  left  to   the 

choice  of  the  operator. 

.  I  first  multiply  by  5,  placing  the  first 
product  figure  one  place  to  the  right;  5  times 
8  is  40;  then  5  times  2  equal  10,  and  the  4 
that  I  carried=14,  write  the  4  under  the  8 ; 
thus  proceed  ;  then  add  the  two  products  for 
the  answer. 


28  PROF.  WARE'S  SYSTEM  OF 

2.  Multiply  8844  by  14. 

8844X14 
35376 


123816 

3.  Multiply  64827  by  30, 

64827X36 
_  §  Commence  with   3,   then 

194481         multiply  that  product  by  2, 
388962      placing  the  first  product  figure 
in  the  place  of  units. 


4.  Multiply  87234  by  39. 

87234X39 


261702 
785106 

3402126 


EQUATION   OF   PAYMENTS.  29 


THE  DIAMOND  OE  CHAIN  BULK 


1st.  Draw  a  perpendicular  line. 

2d.  Arrange  the  numbers  on  opposite  sides 
of  the  line,  as  directed. 

3d.  Then  cancel  on  opposite  sides  of  this 
line  all  equal  figures  and  numbers. 

Mil.  If  there  are  ciphers  on  both  sides  of  the 
line,  cancel  the  same  number  on  eacli  side. 

oth.  If  any  number  on  one  side  will  divide 
any  number  on.  the  opposite  side,  cancel  both 
numbers,  placing  the  quotient  on  the  side- of 
the  larger  number. 

6th.  If  any  two  or  more  numbers  multiplied 
together  equal  one  or  more  numbers  on  the 
opposite  side,  cancel  all  those  numbers. 

tth.  If  any  number  greater  than  unity  will 
divide  two  numbers,  one  on  each  side,  without 
a  remainder,  cancel  both  numbers,  placing  the 
quotients  on  the  right  and  left  of  the  numbers 
divided. 


30  PROF.  WARE'S  SYSTEM  OF 

8th.  Then  multiply  the  figures  that  remain 
on  the  right  hand  for  a  dividend,  and  those 
on  the  left  for  a  divisor. 

Qth.  Then  divide  the  product  of  those  on 
the  right  by  the  product  of  those  on  the  left ; 
the  quotient  arising  from  this  division  will  be 
the  answer. 

REMARKS. 

Should  the  divisor  exceed  the  dividend,  the 
answer  will  be  a  fraction. 

If  the  numbers  will  not  cancel,  then  multi- 
ply those  together  that  are  on  the  right  for  a 
dividend,  and  those  on  the  left  for  a  divisor. 
Then  divide,  and  the  quotient  arising  from 
this  division,  gives  the  answer. 

This  rule  may  be  considered*  as  a  pair  of 
scales  when  exactly  counterpoised;  for  we 
may  add  or  subtract,  multiply  or  divide — in 
fact,  may  do  any  thing  to  one  side,  so  long  as 
we  do  the  same  to  the  other  side ;  for  our  ob- 
ject will  be,  not  to  destroy  the  balance  or 
equilibrium. 

In  this  rule,  also,  the  same  principle  acts  as 
in  the  scales;  for  we  take  those  things,  the 
value  of  which  we  know,  to  ascertain  the 
value  of  those  which  we  do  not  know. 


EQUATION   OF    PAYMENTS.  31 

MULTIPLICATION  OP  PBAOTIOtfS, 

Place  the  numerators,  both  of  the  multi- 
pliers and  multiplicand,  on  the  right,  and  the 
denominators  of  both  on  the  left  of  the  line, 
then  proceed  to  cancel  all  figures  of  equal 
value  on  the  right  and  left;  those  uncanceled 
show  the  answer. 

EXAMPLES. — 1.  Multiply  \  by  f  of  f  off  of 
|  of  f  of  f  of  -J  and  show  the  answer. 

1 
3 


-Ans. 


2.  Multiply  \  by  f  of  f  of  |  of  TV  A.    f 

3.  Multiply  i  of  |  of  f  by  TV  of  ff .  A.    f 

4.  Multiply  1-  of  f  of  f  by  ££  of  H-  A.  TV 

5.  Multiply  f  of  f  by  f  A.    f . 

6.  Multiply  |  of  T4¥  by  TV  of  -&.  A.  TV 

7.  Multiply  I  of  -fr  of  ^T  by  |f  of  $  of  f  A.  TV 

8.  Multiply  i  of  |  of  f  of  |  by  ^  of  &.  A.  ^. 

9.  Multiply  i  of  f  of  |  of  -J  by  f  of  |.  A.  ^. 

10.  Multiply  |  of  f  of  f  by  ^  of  TV  A.  TV 

11.  Multiply  i  of  |  of  TV  of  |  of  4  by  f.  A.    f 

12.  Multiply  J-  of  f  by  f  of  TV  of  |,  A.  TV 


PROF.   WARE  S    SYSTEM    OF 


DIVISION    OF    FRACTIONS. 


Place  the  numerators  of  the  divisor  on  the 
left,  and  the  denominators  on  the  right,  but 
place  the  dividend  as  in  multiplication.  If 
whole  numbers  are  joined  to  a  fraction,  reduce 
as  in  multiplication. 

PKOBLEMS. 

1.   Divide  i  of  $  of  4  by  |  of  T8j  of  f 
1 


0      t 


4-  Ans. 

2.  Divide  J-  by  f  A.    f 

3.  Divide  4-  by  f  A.    2. 

4.  Divide  f  by  f  A.  If 

5.  Divide  ^  by  f.  A.    -|. 

6.  Divide  £  by  f.  A.    |. 

7.  Divide  |  by  f .  A.  If 

8.  Divide  f  of  £  by  £  of  f .  A.  If 

9.  Divide  f-  of  f  of  f  by  f  of  -||.  A.    f . 

10.  Divide  £  of  4-  by  f  ^  A.    1. 

11.  Divide  |  of  |  by  f  A.    f 

12.  Divide  £  of  -J-  by  |-  of  f  A.     1 . 


EQUATION    OF   PAYMENTS.  33 

13.  Divide  f  of  f  by  f  of  5.  A.    f 

14.  Divide  £  ot  £  by  $  of  10.  A.  fa 

15.  Divide  |- of  |  by  f  of  12.  A. -^V 

16.  Divide  £  of  2  by  £  of  4.  A.    1. 

17.  Divide  ±  of  4  by  £  of  8.  A.    1. 

18.  Divide  1£  by  4.  A.    f . 

19.  Divide  2£  by  £  of  5.  A.    1. 

20.  Divide  ^  of  6  by  2f  of  3.  A.    £. 


SAFE   GUIDE   IN   ADDITION. 
RULE. 

In  addition  put  down  the  whole  amount 
until  done.  The  left  hand  figure  shows  the 
amount  to  be  carried  to  the  next  column,  the 
right  shows  the  answer. 

EXAMPLE. 

13467  34 1st  column. 

46329  23  . .  .2cl  -  " 

72548  28.... 3d 

9302  35....4tli 
57831    4.... last   " 
46357    2....  " 


245834  Am. 

N.  B. — In  the  last  addition  put  the  figure 
in  the  right  hand  column. 


TH& 


34  PROF.  WARE'S  SYSTEM  OF 


OOFVEESIOtf  OP  STEELING  MONEY, 
EULE. 

Place  a  cipher  to  the  right  of  the  pence,  di- 
vide by  13 ;  add  the  shillings,  divide  by  20 ; 
then  add  the  pounds.  Multiply  the  whole  by 
40,  and  divide  the  product  by  0.  Point  off  in 
the  answer  one  figure  for  each  decimal. 

EXAMPLE. 

How  many  dollars  are  there  in  £50  7s.  Gd  ? 
12)60 

2,0)7,  5 

50  375 

40 

9)2015000 


$223.88.8    par  value. 
SOLUTION. 

Multiply  by  40,  because  in  £1  there  are  40 
sixpences ;  divide  by  9,  because  $1  is  equiva- 
lent to  4s.  6d.  at  par.  In  4s.  Gd.  there  are  0 
sixpences. 


EQUATION   OF   PAYMENTS.  35 


BARTER. 


Place  the  given  quantity  of  the  commodity 
and  the  price  at  which  it  is  valued,  on  the 
right  of  the  line.  Place  on  the  left  the  con- 
stituents of  the  commodity  whose  value  is 
required. 

EXAMPLES. 

1.  How  much  cloth  at  22  cents  per  yard, 
must  be  given  i:i  exchange  for  4400  Ibs.  of 
cotton,  at  3^-  cents  per  pound  ? 


700  Ans.  700  yds. 

2.  How  much  tea,  at  G4  cents  per  pound, 
must  be  given  for  448  pounds  of  coffee,  at  20 
cants  per  pound  ?  Ans.  140  Ibs. 

3.  How   much   wheat   at   $1.25   cents  per 
bushel,  must  be  given  for  fifty  bushels  of  rye, 
at  70  cents  per  bushel  ?  Ans.  28  bush. 

4.  How  many  bushels  of  rye  worth  70  cents 
per  bushel,  must  I  give  for  28  bushels   of 
wheat,  the  wheat  valued  at  $1.25  per  bushel  ? 

Ans.  50  bush. 


36  PROF.  WARE'S  SYSTEM  OF 

5.  How  many  pounds  of  coffee  can  I  have  in 
exchange  for  28  Ibs.  of  butter,  valued  at  21 
cents  per  lb.;  the  value  of  the  coffee  is  12  cts. 
per  lb  ?  Ans.  49. 

G.  How  many  sheep  at  $4  per  head,  must  I 
give  for  6  cows,  at  $12  a  piece  ?  Ans.  18. 

7.  Sold  28  bushels  of  wheat  at  75  cents  per 
bushel;  how  many  barrels  of  salt  can  I  have 
in  exchange  at  $2  per  barrel  ?         Ans.  10-J. 

8.  How  much  coffee  at  20  cents  per  pound, 
must  I  give  for  120  yards  of  cloth,  at  64  cents 
per  yard  ?  Ans.  384. 

9.  How  many  bushels  of  wheat  will  pay  for 
40  barrels  of  pork  at  $8  per  barrel,  when  wheat 
is  worth  80  cts.  per  bushel  ?     Ans.  400  bush. 


DISCOUNT. 

Discount  is  an  allowance  made  for  prompt  payment. 
DISCOUNT   WITHOUT  TIME. 

Place  the  sum  on  which  the  discount  is  to 
be  made,  and  the  rate  per  cent,  on  the  right, 
and  one  hundred  on  the  left. 

EXAMPLE. — What  is  the  discount  on  $400, 
at  6  per  cent Ans.  $24. 


EQUATION   OF   PAYMENTS. 


WOOD  MEASURE,  &c. 
RULE. 

Place  the  length,  height,  and  width,  on  the 
right ;  on  the  left  place  the  dimensions  of  one 
cord. 

EXAMPLE. 

How  many  cords  of  wood  in  a  pile  120  feet 
long,  12  feet  high,  and  4  feet  wide  ? 

15 
3 

Ans.  45  Cords. 
SOLUTION. 

4  equals  4;  4  into  12  three  times;  8  into 
120,  15  times;  3  times  15  is  45  cords. 

How  many  cords  of  wood  in  a  pile  32  feet 
long,  12  high,  and  4  wide  ? 

4 

3 

Ans.  12  Cords. 
How  many  yards  of  carpeting  will  it  take 
to  carpet  a  hall  18  by  20  feet  ? 

J9  2 

20 

Ans.  40  Yards. 
NOTE. — Divide  by  9,  because  9  square  feet 
make  1  square  yard. 


38 


PRCF.  YvT ARE'S    SYSTEM   OF 


If  -J  of  6  be  3,  what  will  the  4-  of  20  be  ? 


3 
3 
1 

20 

Ans. 


How  many  bricks  in  a  wall  40  feet  long,  12 
feet  high,  and  1£  feet  thick  ?  Size  of  brick,  8 
by  4  by  2  inches. 

8  40 
4  12 
3  I  4 
2  I  1728  in.=  1  cubic  ft. 

Answer  17,280  brick*. 

How  many  feet  board  measure  in  the  floor 
joists  of  a  building  18  by  40  feet,  joists  3  by  8 
inches,  placed  16  inches  apart  from  the  centre 

of  each  ? 

I  40 

I  18 

16  I    3 

I    8 

Ansicer  WOO  feet. 

How  many  dollars  will  it  cost  to  carpet  a 
hall  24  by  15,  carpet  one  yard  wide,  at  11 
shillings  per  yard  ? 


24 
15 
11 


Answer  $55 


EQUATION   OF   PAYMENTS.  39 


IV  A.  M  E  S     OF 

.     BRAZIL.  D    c  M 

Johannes,  (half  in  proportion)  17  00  8 

Dobraon 32  71  4 

Dobra 1 7  SO  5 

Moidore,  (half  in  proportion) G  56 

Crusado 63  8 

ENGLAND. 

Guinea,  half  in  proportion 5  11  6 

Sovereign,  do  485 

Seven  Shilling  Piece 1  70  6 

FRANCE. 

Double  Louis,  coined  bef.  1786 9  69  3 

Louis,  coined  before  1786 4  84  4 

Double  Louis,  coined  since  1786 9  16  3 

Louis,  coined  since  1786 4  58  1 

Double  iNapoleon,  or  forty  francs 7  71  3 

Napoleon,  or  twenty  francs 3  86  6 

COLUMBIA. 

Doubloons 15  53  8 

MEXICO. 
Doubloons,  shares  in  proportion 15  53  8 

PORTUGAL. 

Dobraon  .  . S3  71  4 

Dobra 17  35  6 

Johannes 17  06  8 

Moidorc,  half  in  proportion 6  56 

Piece  of  16  testoons,  or  1000  rees 3  12  5 

Old  Crusado  of  400  rces 58  6 

New  Crusado  of  480  rees 63  7 

Millree,  coined  in  1755 78 


40        .  PROF.  WARE'S  SYSTEM  OF 

SPAIN. 

D     C   M 

Quadruple  pistol,  or  Doubloon,  1772,  double 

and  single,  and  shares  in  proportion 16  03  3 

Doubloon,  1801 15  53  8 

Pistole,  1801 3  88  8 

Coronilla,  gold  doll.,  or  vintem,  1801 98  2 

U.  S.  AMERICA. 

Eagle,  coined  before  July  31, 1834 10  66  8 

Eagle,  coined  after  July  31,  1834 10  . .    . 

Shares  in  proportion. 


VALUE  OF  FOREIGN  MONEY. 

CANADA,  NOVA  SCOTIA,  &c. 

A  Farthing ,. 4.1 

4  Farthings  =  a  penny 1       Gf 

12  Pence  a  shilling 20 

60  Pence  a  dollar 1 

20  Shillings  a  pound 4 

30  Shillings  a  moidore 6 

40  Shillings  a  half  Joe 8     .. 

50  Shillings  a  Fed.  Eagle 10     . . 


EQUATION   OF   PAYMENTS.  41 

NORTHERN  PARTS 

ENGLAND  &  SCOTLAND. 

LONDON,   LIVERPOOL,  BRISTOL,  EDINBURGH,   GLASGOW,   JbC. 

D          C  M 

A  Farthing 4.6 

2  Farthings  ==  a  half-penny 9£ 

2  Half-pence       a  penny 1  8£ 

4  Pence  a  groat 7  4 

G  Pence  a  half  shilling 11  1.1 

12  Pence  a  shilling 22  2.2 

54  Pence  an  Ame.  dol 1     . . 

5  Shillings          a  crown 1     11  1.1 

20  Shillings  a  pound  ster 4    44  4.4 

21  Shillings          an  English  guinea ...     4    66  6.7 

BREMEN. 

3  Grotes  =  a  double  shilling.    .  .       32 

24  Grotes  a  mark 25  5| 

48  Grotes  a  double  mark 51  1 

72  Grotes  or  3  marks  a  rix  dollar 76  6£ 

Accounts  are  kept  in  Rix-dollars  and  Grotes. 
HANOVER, 

LUNENBURG,  ZELL,  &C. 

A  Pfenning 2.7 

3  Pfennings      =  a  dreyer 8        .2 

8  Pfennings  a  marien 2      1.9 

12  Pfennings  a  grosh 3      2.8 

8  Groshen  ahalfguilden 26      2£ 

16  Groshen  a  guilclen 52      5 

24  Groshen  a  rix  dollar 78      7i 

32  Groshen  a  double  guilden  . .     1      5 

34  Groshen  a  ducat 1     10 

Accounts  are  kept  in  Rix-dollars,  Groshens,  and 
Pfennings. 


42  PROF.  WARE'S  SYSTEM  OF 

EUBOPE. 

SOUTHERN   PARTS. 

PORTUGAL. 

r>      c        M 

A  Rhea 1* 

10  Reas           =  a  half  vintin. 1  l£ 

20  Reas                a  vintin . .  2  5 

5  Vintins           a  testoon 12  5 

4  Tcstoons        a  crusad  of  exchange .    ..  50 

24  Vintins  a  new  crusado 60 

10  Testoons        a  milrea 1    25 

48  Testoons         a  moidore 6 

64  Testoons         a  Johannes 8 

Accounts  are  kept  in  Millreas  and  Reas. 

FRANCE    AND    NAVARRE. 

PARIS,  LYONS,  MARSEILLES,  BORDEAUX,  BAYONNB,  &C. 

y 

A  Denier Of 

3  Deniers       =  aliard... 2.3 

2  Liards  a  dardene 4.6 

12  Deniers  a  sol 9£ 

20  Sols  a  livre  tournois 18  5 

60  Sols  an  ecu  of  exchange ....     55  5 

6  Livres  an  ecu  or  crown 1       11  1.1 

10  Livres  a  pistole 1      85 

24  Livres  a  Louis  d' or •. . . .     4      44    4.4 

Accounts  are  kept  in  Livres,  Sous,  and  Deniers. 
SPAIN. 

32  Reals  =  a  pistole  of  exchange 3     18      5 

36  Reals         a  pistole 3    72      2 

Accounts  are  kept  in  Dollars,  Reals,  &  Maravedis. 


EQUATION   OF   PAYMENTS.  43 


SPAIN — Continued. 

GIBRALTAR,   MALAGA,   DENIA,    &C. 

Velon. 

D         C  M 

A  Maravedi 1.6 

2  Maravedis  =  an  ochavo 3.2 

4  Maravedis         a  quartil 6.4 

34  Maravedis         a  real  velon 5  3.2 

15  Reals  a  piastre  of  ex 79  C.3 

512  Maravedis         a  pistole 77  6.3 

60  Reals  a  pistole  of  ex. ...     3    18  5 

2043  Maravedis         a  pistole  of  ex. ...     3    18  5 

70  Reals  a  pistole 3    72  2 

Accounts  are  kept  in  Dollars,  Reals,  &  Maravedis. 


BARCELONA,  SARAGOSSA,  VALENCIA,  &C. 

A  Maravedi 3.9 

16  Maravedis  =  a  soldo 6      2£ 

2  Soldos  a  rial,  old  plate 12      5 

16  Soldos  a  dollar 1 

20  Soldos  alibra 1  25 

24  Soldos  a  ducat 1  50 

60  Sold®s  a  pistole 3  60 

There  are  also  Ducats  of  21  and  22  Soldos. 
Accounts  are  kept  in  Dollars,  Reals  &  Maravedis. 

Note.— Although  60  Soldos  are  equal  to  8-  dollars 
and  75  cents,  the  Spanish  Pistole  is  worth  but  3  doll- 
ars and  60  cents. 


44  PROF.  WARE'S  SYSTEM  OF 

ITALY. 

GENOA,  NOVA,  CORSICA,  BASTEA,  &C. 

D         C  M 

A  Denari 6£ 

12  Denari  =  a  soldi 7.9 

4  Soldi  a  clievalet 3  1.8 

20  Soldi  a  lira 15  9.2 

30  Soldi  a  testoon. 23  8| 

5  Lires  a  croisade 79      6.3 

115  Soldis          apezzoofex 92      5.9 

6  Testoons     a  genoine 1     44      4 

20  Liers  a  pistole 3    18      5 

Accounts  are  kept  in  Liers,  Soldis,  and  Denaris. 

CHINA. 

PEKIN,   CANTON,    &C. 

A  Cash 1.4 

10  Cash     =     a  candareen 1      4.8 

10  Candareens  a  mace 14      8 

10  Mace,  1  oz.  6  dwt.    6  grs.  =  a  tale.     1    48 

Accounts  are  kept  here  in  Tales,  Mace,  Candareens, 
and  Cash. 


EQUATION   OF   PAYMENTS.  45 

Prof.  W,  POWELL  WAEE'S 

MAGIC   SQUARE. 


These  columns  (added)  make  100,  forty-two 
different  ways. 

13796284137962841379 
39172468391724683917 
71938642719386427193 
97314826973148269731 
62841379628413796284 
24683917246839172468 
86427193864271938642 
48269731482697314826 
13796.  284137962841379 
391724683917246839  17 
71938642719386427193 
97314826973148269731 
62841379628413796284 
24683917246839172468 
86427193864271938642 
48269731482697314826 
13796284137962841379 
39172468391724683917 
71938642719386427193 
973148269  7  3148269731 


46  PROF.  WARE'S  SYSTEM  OF 


PROF.  WARE'S  CHALLENGE. 


From  N.Y.  Herald,  Oct.  30,  1870. 

$10  000  has    '">aori    ^oT\neifort   irifVi    n.roon'hflnm    "Rrr>e 


Numerous  extracts  from  different  sections  of  the  country 
omitted  for  want  of  space. 


From  N.Y.  Standard,  Nov.  4tli,  1870. 

A  CHANCE  TOR  MATHEMATICIANS.  -  The  problem  of  the 
Equation  of  Payments  is  receiving  at  present  the  attention  of 
the  best  mathematicians,  an  announcement  h-iving  been  re- 
cently made  by  Prof  W  POWELL  WAKE,  of  21  West  124th  Street 
of  this  city  that  he  would  pay  $10  000  for  the  best  rule.'  The 
money  has  been  deposited  for  the  purpose  with  Me"crs.  Gm  n- 
baum  Bros  &  Co..  Bankers,  National  Park  Bank  Bnildinir.  to 
whom  competitors  may  send  their  rules.  On  December  1st  the 
successful  competitor  will  receive  payment  for  his  rule. 

From  N.Y.  World,  Nov.  13,  1870. 

The  mathematicians  have  become  very  enthusia«»ic  in  their 
race  for  the  $10,000  offered  by  Prof.  WARE,  of  this  city,  for  the 
best  rule  for  the  Equation  of  Payments.  The  plans  already 
received  come  from  almost  every  section  of  the  country,  and 
include  some  very  good  and  some  very  preposterous  solution-. 
All  parties  interes  ed  will  meet  at  12  o'clock,  on  December  1. 
1870,  at  the  Astor  House,  at  which  time  the  successful  compet- 
itor will  receive  the  reward  for  his  labor. 

From  N.Y.  Times,  Nov.  15,  1870. 

EQUATION  OF  PAYMENTS.— Prof.  WARE'S  offer  of  $10.000 
for  the  best  rule  for  the  equation  of  payments  has  drawn  or.1"  n 
very  exciting  competition  between  the  mathematicians  fill  over 
the  country.  The  rules  already  received  by  Prof.  WAKE  anl 
the  Messrs.  GREENBUM  BROTHERS,  in  whose  hands  the  money 
is  doposited,  come  from  every  section  of  the  country. a:1  d  in- 
clude some  marvelous  mathematical  efforts.  The  award  for  the 
best  plan  will  be  made  December  1,  1870,  at  the  Astor Hou>e.  at 
which  place  all  interested  parties  will  assemble  at  12  o'clock. 


EQUATION  OF  PAYMENTS.  47 


DECISION  OF  THE  JUDGES. 

[TRUE  COPY.] 

We,  the  undersigned  committee  selected  to  decide 
upon  the  different  plans  submitted  in  the  contest  for 
the  best  rule  for  the  Equation  of  Payments,  after  ma- 
ture and  careful  examination  and  test  of  plans  offered 
by  fifty-seven  competitors  (made  conjointly  and  per- 
sonally) do  declare  this  to  be  our  positive  and  final 
decisions,  viz  : 

That  the  Rule  presented  by  Prof.  W.  POWELL 
WARE,  of  New  York  City,  is  the  shortest,  simplest, 
and  best,  possessing  the  greatest  utility  and  general 
adaptation,  not  only  of  the  plans  now  before  us,  but 
of  any  that  has  ever  come  to  our  knowledge,  and 
which  in  our  judgment  is  mathematically  correct. 

We  therefore  declare  that  Prof.  W.  POWELL  WAKE, 
of  New  York,  is  duly  entitled  to  the  award  offered. 
SIGNED  : 

Jos.  C.  Atwood,  with  Landers,  Frary  &  Clark,  53 
Chambers  Street. 

A.  O.  Field,  with  Jordan,  Marsh  &  Co.,  184  and  186 
Church  Street. 

John  G.  Huhn,  with  Hoover,  Calhoun  &  Co.,  3C2 
Broadway. 

Edward  F.  Choate,  with  E.  R.  Dibble  and  Co.,  53 
and  55  W^rth  Street. 

Ji.  F.  Blake,  with  Manning,  Glover  &  Co.,  109  and 
111  Worth  Street. 

We  fully  concur  in  the  above  decision — 

H.  E.  'Phelps,  book-keeper  of  H.  B.  Claflin  &  Co, 
John  P.  Gaul,  with  Tefft,  Griswold  &  Kellogg. 

443  find  445  Broadwav 
Anthoii  J.  Kruger, with  Duncan, Sherman  &  Co., 

Bankers. 
Wm.  H.  Clark,  with  Henry  Clewes  &  Co.,  Bankers, 

32  Wall  Street. 
Matthew  Bunker,  of  Benedict,  Hall  &  Co.,  134  and 

136  Grand  Street. 


N.  B. — The  foregoing  rules  are  equally  adapted  to 
pounds,  shillings,  and  pence,  by  calling  the  pounds 
so  many  dollars,  and  calling  the  shilling  another 
pound  or  dollar  if  10s.  or  upward.  Thus:  £10,  15s., 
read  $11 ;  £9,  6s.,  read  $9.  &c. 


RANKIFS  PERPETUAL  ALMANAC, 


BOOK  FORM, 


TWO  MONTHS  TO  A  PAGE. 


PHILADELPHIA : 
CLAXTON,  REMSEN  &  HAFFELFINGER, 

624,  626  &  628  MARKET  STREET. 


Entered  according  to  Act  of  Congress,  in  the  year  1873,  by 

A.  N.  RANKIN, 
In  the  Office  of  the  Librarian  of  Congress,  at  Washington. 


ELECTROTYPED  BY  J.  PAGAN  &  SON,  PHILADELPHIA. 


Mo.  |  Tu,  |  We.  Th.  |  Fr.  |  Sat  |  g. 

|  7  |  14  |  21  |  28 

Tu.  |  We.  |  Th.  |  Fr.  |  Sat.  |  g.  |  Mo. 

1  |  8  |  15  |  22  |  29 

We.  |  Th.   Fr.  |  Sat.  |  S.  |  Mo.  |  Tu. 

2  |  9  |  16  |  23  |  30 

Th.  |  Fr.  j  Sat.  |g.  |  Mo.  |  Tu.  |  We. 

3  |  10  |  17  j  24  |  31 

Fr.  |  Sat.   S.  |  Mo.  |  Tu.  |  We.  |  Th. 

4  |  11  |  18  |  25  | 

Sat.  |S.  |  Mo.  |  Tu.  |  We.  |  Th.  |  Fr. 

5  |  12  |  19  |  26  | 

S.  I  Mo.  |  Tu.  |  We.  |  Th.  |  Fr.  |  Sat. 

6  |  13  |  20  |  27  | 

1771  |  1772  |     |  1773  |  1774  |  1775  |  1776 

January. 

|  1777  |  1778  |  1779  |  1780  |     |  1781 

1782  |  1783  |  1784  |     |  1785  |  1786  |  1787 

1788  |     |  1789  |  1790  |  1791  |  1792  | 

1793  |  1794  |  1795  |  1796  |     |  1797  |  1798 

1799  |  1800  |  1801  |  1802  |  1803  |  1804  | 

1805  |  1806  |  1807  |  1808  |     |  1809  |  1810 

1811  |  1812  |     |  1813  |  1814  |  1815  |  1816 

j  1817  1818  |  1819  j  1820  |     |  1821 

1822  |  1823  1824  |     |  1825  |  1826  |  1827 

1828  |     |  1829  |  1830  |  1831  |  1832  | 

1833  |  1834  |  1835  1836  |     |  1837  |  1838 

1839  |  1840      |  1841  |  1842  |  1843  |  1844 

|  1845  |  1840  |  1847  |  1848  |     |  1849 

1850  |  1851  |  1852  |     |  1853  |  1854  |  1855 

1856  |     |  1857  |  1858  |  1859  |  1860  | 

1861  |  1862  1863  |  1864  |     |  1865  |  1866 

1867  |  1868  |     |  1869  |  1870  |  1871  |  1872 

|  1873  |  1874  |  1875  |  1876)     |  1877 

1878  |  1879  |  1880  |     |  1881  |  1882  |  1883 

1884  |     |  1885  18S6  |  1887  |  1888  | 

1889  |  1890  |  1891  1892  |     |  1893  |  1894 

1895  |  1896  |      1897  |  1898  |  1899  |  1900 

1901  |  1902  |  1903  1904  |     |  1905  |  1906 

1907  |  1908  |      1909  |  1910  |  1911  |  1912 

|  1913  |  1914  1915  |  1916  |     |  1917 

1918  |  1919  |  1920  |     |  1921  |  1922  |  1923 

1924  |     |  1925  |  1926  |  1927  |  1928  | 

1929  |  1930  |  1931  |  1932  |     |  1933  |  1934 

1935  |  1936  |     |  1937  |  1938  |  1939  |  1940 

|  1941  |  1942  1943  |  1944  |     |  1945 

1946  |  1947  |  1948      |  1949  |  1950  |  1951 

1952  |     |  1953  19n4  |  1955  |  1956  | 

February. 

Mo,  |  Tu.   We.  Th.  |  Fr.  |  Sat.  |  S. 

|  4  |  11  |  18  |  25 

Tu.  |  We.  Th.   Fr.  |  Sat.  |  S.  1  Mo. 

|  5  |  12  j  19  |  26 

We.  |  Th.   Fr.   Sat.  |  S.  1  Mo.  |  Tu. 

|  6  |  13  |  20  |  27 

Th.  |  Fr.   Sat.  S-  I  Mo.  |  Tu.  |  We. 

|  7  |  14  |  21  |  28 

Fr.  |  Sat.  S.   Mo.  |  Tu.  |  We.  |  Th. 

1  |  8  |  15  j  22  j  29 

Sat.  |S.  |  Mo.  |  Tu.  |  We.  |  Th.  |  Fr. 

2  |  9  |  16  |  23  | 

S.  |  Mo.  |  Tu.  |  We.  |  Th.  |  Fr.  |  Sat. 

3  |  10  |  17  |  24  j 

The  Year  and  Days  of  the  Week  for  both  Months  are  in  the  same  column. 

|  4|11J18|26 

Mo.  |  Tu.  |  We.  Th.   Fr.  |  Sat.  |  S- 

|  5  |  12  j  19(26 

Tu.  |  We.  |  Th.   Fr.  |  Sat.  |  g.  |  Mo. 

|  6  |  13  |  20  |  27 

We.  |  Th.  |  Fr.   Sat.  |  S.  1  Mo.  |  Tu. 

|  7|14|21|2S 

Th.  |  Fr.  |  Sat.   g.  |  Mo.  |  Tu.  |  We. 

1  |  8  |  15  |  22  |  29 

Fr.  |  Sat.  |  S.   Mo.  |  Tu.  |  We.  |  Th. 

2  |  9  |  16  |  23  |  30 

Sat.  |S.  1  Mo.  Tu.  |  We.  |  Th.  |  Fr. 

3  |  10  |  17  |  24  |  31 

S.  1  Mo.  |  Tu.   We.  |  Th.  j  Fr.  |  Sat. 

March. 

1771  |     |  1772  |  1773  |  1774  |  1775  | 

1776  |  1777  |  1778  1779  |     |  1780  |  1781 

1782  |  1783  |      1784  |  1786  |  1786  |  1787 

|  1788  |  1789  1790  |  1791  |     |  1792 

1793  j  1794  |  1795    jj  1796  |  1797  |  1798 

1799  |  1800  |  1801  1802  |  1803  |     |  1804 

1805  |  1806  |  1807      |  1808  |  1809  |  1810 

1811  |     |  1812  1813  |  1814  |  1815  | 

1816  |  1817  |  1818  1819  |     |  1820  |  1821 

1822  |  1823  |      1824  |  1825  |  1826  |  1827 

|  1828  |  1829  1830  |  1831  |     |  1832 

1833  |  1834  |  1835  1     |  1836  |  1837  |  1838 

1839  j     |  1840  |  1841  j  }842  j  1843  | 

1844  |  1845  |  1846  |  1847  |     |  1848  |  1849 

1850  |  1851  j     j  1852  |  1853  |  1854  |  1855 

|  1856  |  1857  |  1858  |  1859  |     |  I860 

1861  |  1862  |  1863  |     |  1864  |  1865  |  1866 

1867  |     |  1868  |  1869  |  1870  |  1871  | 

1872  |  1873  |  1874  |  1875  |     |  1876  |  1877 

1878  |  1879  |     |  1880  |  1881  |  1882  |  1883 

j  1884  |  1885  |  18^6  |  1887  |     |  1888 

1889  |  1890  |  1891  |     |  1892  |  1893  |  1894 

1895  |     |  1896  |  1897  |  1898  |  1899  |  1900 

1901  |  1902  |  1903  |     |  1904  |  1905  |  1906 

1907  |     |  1908  |  1909  |  1910  |  1911  | 

1912  |  1913  |  1914  j  1915  |     |  1916  |  1917 

1918  |  1919  |     |  1920  (  1921  |  1922  j  1923 

|  1924  |  1925  |  1926  |  1927  |     |  1'.rj> 

1929  |  1930  |  1931  |     |  1932  |  1933  |  1934 

1935  |     |  1936  |  1937  |  1938  |  1939  | 

1940  |  1941  |  1942  1943  |     |  1944  |  1945 

1946  |  1947  |     |  1948  |  1949  |  1950  |  1951 

April. 

|  1952  |  1953  |  1954  |  1955  |     |  1956 

1|  8  |  15  |  22  (29 

Mo.  |  Tu.  |  We.  |  Th.  |  Fr.  |  Sat.  |  g. 

2  |  9  |  16  |  23  |  30 

Tu.  |  We.  |  Th.   Fr.  |  Sat.  |  g.  J  Mo. 

3  |  10  |  17  |  24  | 

We.  |  Th.  |  Fr.   Sat.  |  S.  1  Mo.  |  Tu. 

4  |  11  |  18  |  25  | 

Th.  |  Fr.  |  Sat.   g.  (  Mo.  |  Tu.  |  We. 

5  |  12  |  19  |  26  | 

Fr.  |  Sat.  |  S.   Mo.  |  Tu.  |  We.  |  Th. 

6  |  13  |  20  |  27  | 

Sat.  |  g.  |  Mo.  Tu.  |  We.  |  Th.  |  Fr. 

7  |  14  |  21  |  28  | 

S.  |  Mo.  |  Tu.   We.  |  Th.  |  Fr.  |  Sat. 

The  Year  and  Days  of  the  Week  for  both  Months  are  in  the  same  column. 

Mo.  Tu.   We.  |  Th.  |  Fr.  |  Sat.  |  g. 

|  6  |  13  |  20  |  27 

Tu.  |  We.  Th.  |  Fr.  |  Sat.  |  g.  |  Mo. 

|  7  |  14  |  21  |  28 

We.  j  Th.   Fr.  |  Sat.  |  S.  1  Mo.  |  Tu. 

1  |  8  |  15  !  22  |  29 

Th.  |  Fr.   Sat.  j  g.  |  Mo.  |  Tu.  |  We. 

2  |  9  |  16  |  23  |  30 

Fr.   Sat.   g.  |  Mo.  |  Tu.  |  We.  |  Th. 

3  |  10  |  17  |  24  |  31 

Sat.  |  S.   Mo.  |  Tu.  |  We.  |  Th.  |  Fr. 

4  |  11  |  18  |  25  | 

S.   Mo.   Tu.  |  We.  |  Th.  |  Fr.  |  Sat. 

5  |  12  j  19  |  26  | 

1771  |      1772  |  1773  |  1774  |  1775  | 

May. 

1776  |  1777  1778  |  1779  |     |  1780  |  1781 

1782  |  1783  |     |  1784  |  1785  |  1786  |  1787 

|  1788  |  1789  |  1790  |  1791  |     |  1792 

1793  !  1794  |  1795  |     |  1796  |  1797  |  1798 

1799  |  1800  |  1801  |  1802  |  1803  |     |  1804 

1805  1806  |  1807  |     |  1308  |  1809  |  1810 

1811  |     |  1812  |  1813  |  1814  |  1815  | 

1816  |  1817  |  1818  |  1819  |     |  1820  |  1821 

1822  |  1823  |     |  1824  |  1825  |  1826  |  1827 

|  1828  |  1829  |  1830  |  1831  |      1832 

1833  |  1834  |  1835  1     |  1836  |  1837  |  1838 

1839  j     |  1840  |  1841  |  1842  |  1843  | 

1844  |  1845  |  1846  |  1847  |     |  1848  |  1849 

1850  |  1851  |     |  1852  |  1853  |  1854  |  1855 

|  1856  |  1857  |  1858  |  1859  [     |  1860 

1861  |  1862  |  1863  |     |  1864  |  1865  1866 

1867  |     |  1868  |  1869  |  1870  |  1871 

1872  |  1873  |  1874  |  1S75  |     |  1876  |  1877 

1878  |  1879  |     |  1880  |  1881  |  1882  |  1883 

|  1884  |  1885  |  18^6  |  1887  |     |  1888 

1889  |  1890  |  1891  |     |  1892  |  1893  |  1894 

1895  |     |  1896  |  1897  |  1898  |  1899  |  1900 

1901  |  1902  1903  |     |  1904  |  1905  |  1906 

1907  |     |  1908  |  1909  |  1910  |  1911  | 

1912  |  1913  |  1914  |  1915  |      1916  |  1917 

1918  |  1919  |     |  1920  |  1921  1922  |  1923 

|  1924  |  1925  |  1926  |  1927      |  1928 

1929  |  1930  |  1931  |     |  1932  1933  |  1934 

1935  |     |  1936  |  1937  |  1938  1939 

1940  |  1941  |  1942  |  1943  |      1944  1945 

1946  |  1947  |     1  1948  |  1949  1950  1951 

1952  |  1953  |  1954  |  1955  |      1956 

June. 

Mo.  Tu.  |  We.  |  Th.  |  Fr.  |  Sat.  g. 

|  3|10|17|24 

Tu.   We.  |  Th.  |  Fr.  |  Sat.  |  S.   Mo. 

|  4  |  11  |  18  |  25 

!We.  Th.   Fr.  |  Sat.  |  S.  1  Mo-  Tu- 

|  5  |  12  |  19  |  26 

fh.   Fr.  |  Sat.  IS-  I  Mo.  |  Tu.   We. 

|  6  |  13  |  20  |  27 

Fr.   Sat,  |S.  |  Mo.  |  Tu.  |  We.  Th. 

|  7|14|21|28 

Sat.   S.  1  Mo-  1  Tu-  1  We-  1  Th-  !  Fr- 

1  |  8  |  15  |  22  |  29 

S.   M<>.   Tu.  |  We.  |  Th.  |  Fr.  |  Sat. 

2  |  9  |  16  |  23  |  30 

\  The  Year  and  Days  of  the  Week  for  both  Months  are  in  the  sume  column 

1  |  8  |  15  j  22  |  29 

Mo.  |  Tu.   We.  |  Th.  |  Fr.  |  Sat.  |  S- 

2  |  9  |  16  |  23  |  30 

Tu.   We.  |  Th.  |  Fr.  |  Sat.  |  S-  1  Mo 

3  |  10  |  17  24  |  31 

We.  Th.   Fr.   Sat.  |  S.   Mo.  |  Tu. 

4  |  11  |  18  |  25  | 

Th.   Fr.   Sat.   g.  |  Mo.  |  Tu.  |  We. 

5  |  12  j  19  26  | 

Fr.   Sat.   S-   Mo.  |  Tu.  |  We.  |  Th. 

6  |  13  |  20  |  27  | 

Sat.   S.   Mo.   Tu.  j  We.  |  Th.  |  Fr. 

7  |  14  |  21  |  28  | 

S.   Mo.   Tu.   We.  |  Th.  |  Fr.  |  Sat. 

July. 

1771      1772  1773  |  1774  |  1775  | 

I 

1776  1777  1778  |  1779  |     \  1780  |  1781 

1782  1783  |     |  1784  |  1785  |  1786  |  1787 

1788  |  1789  |  1790  |  1791  |     |  1792 

1793  1794  |  1795      |  1796  1797  |  1798 

1799  1800  |  1801  |  1802  |  1803  |     |  1804 

1805  1806  |  1807  |     |  1808  |  1809  |  1810 

1811      |  1812  |  1813  |  1814  |  1815  | 

1816  |  1817  |  1818  |  1819  |     |  1820  |  1821 

1822  |  1823  |      1824  |  1825  |  1826  |  1827 

|  1828  |  1829  |  1830  |  1831  |     |  1832 

1833  |  1834  |  1835  |     |  1836  |  1837  |  1838 

1839  |     |  1840  |  1841  |  1842  |  1843  | 

1844  |  1845  |  1846  |  1847  |     |  1848  |  1849 

1850  |  18ol  |     |  1852  |  1853  |  1854  |  1855 

|  1856  |  1857  |  1858  |  1859  |     |  1860 

1861  |  1862  |  1863  |     |  1864  |  1865  |  1866 

1867  |     |  1868  |  1869  |  1870  |  1871  | 

1872  |  1873  1874  |  1875  |      1876  |  1877 

1878  |  1879  |     |  1880  |  1881  1882  |  1883 

188-t  1885  |  18*6  |  1887      |  1888 

1889  1890  |  1891      |  1892  1893  |  1894 

1895  |     |  1896  |  1897  |  1898  1899  |  1900 

1901  1902  1903  |     |  1904  1905  |  1906 

1907  |     |  1908  |  1909  |  1910  1911  | 

1912  |  1913  |  1914  !  1915  |      1916  |  1917 

1918  |  1919  |      1920  |  1921  1922  |  1923 

|  1924  |  1925  |  1926  |  1927  |     |  1928 

1929  |  1930  |  1931  |     |  1932  |  1933  |  1934 

1935  |     |  1936  |  1937  |  1938  |  1939  | 

1940  1  1941  |  1942  |  1943  |     |  1944  |  1945 

1946  |  1947  |     |  1948  |  1949  |  1950  |  1951 

August. 

|  1952  |  1953  |  1954  |  1955  |     |  1956 

|  5  |  12  |  19  |  2rt 

Mo.  |  Tu.   We.  |  Th.  |  Fr.  |  Sat.  |  g. 

|  6|13|20|--T 

Tu.  1  We.  Th.   Fr.   Sat.  |  S-  1  Mo. 

|  7  |  14  |  21  |  28 

We.  |  Th.   Fr.   Sat.   S.  1  Mo.  |  Tu 

1|  8  |  15  (22  (20 

Th.  1  Fr.   Sat.   S-   Mo.  |  Tu.  |  We 

2  |  9  |  10  |  23  |  HO 

Fr.  |  Sat,  S.   Mo.   Tu.  |  We.  |  Th. 

3  |  10  |  17  |  2H  31 

Sat.  |  S,   Mo.   Tu.   We.  |  Th.  1  Fr. 

4  |  11  j  18  |  25  | 

S.  |  Mo.   Tu.   We.  Th.  |  Fr.  |  Sat. 

The  Year.and  Daya.of  the  Week  for  both  Months  are  in  the  same  column. 

j 
i 

Mo.  |Tu.  |  We.  |Th.  |  Fr.  |  Sat  |  S. 

j  2  |  9  1  16  |  23  |  30 

Tu.   We.  Th.  |  Fr.  |  Sat.  |  S.  1  Mo. 

I  3  j  10  1  17  |  24  | 

We.  |  Th.  1  Fr.  |  Sat.  |  <S.  |  Mo.   Tu. 

I  4  1  11  1  18  |  25  | 

Th.   Fr,  j  Sat.  |  &.  |  Mo.  |  Tu.   We. 

5  |12|  19  |26| 

Fr.  |  Sat.   g.  |  Mo.  |  Tu.   We.  |  Th. 

1  «>  |  13  |  20  I  27  | 

Sat.   S.  j  Mo.  |  Tu.  |  We.  |  Th.  |  Fr. 

|  7  |  14  |  21  j  28  | 

S.  I  Mo.  |  Tu.  |  We.  |  Th.  |  Fr.  |  Sat 

1  |  8  1  15  |  22  |  29  | 

1771  |     |  1772  |  1773TT774TI77T 

September. 

1-76  |  1«7  1778  |  1779)     J  1780  |  1781 

• 

1/82  |  1783  |     |  1784  |  1735  |  1786  |  1787 

|  1788  1789  |  1790  |  1791  |     |  1792 

1/93  |  1794  |  1795  |     |  1796  1797  |  1798 

1799  |  1800  |  1801  |  1802  |  1803  |     |  1804 

1805  |  1806  |  1807      |  1808  |  1809  |  1810 

1811  |     |  1812  |  1813  |  1814  j  1815 

1816  |  1817  |1818  |  1819J     |  1820  |  1821 

1822  |  1823  |     |  1824  |  1825  1826  |  1827 

|  1828  1829  |  1830  |  1831  |      1832 

1833  |  1834  |  1835  |     |  1830  |  1837  |  1838 

1839  J      1840  |  1841  |  1842  |  1843  | 

1844  |  1845  1846  |  1847  |     |  1848  |  1849 

1850  j  1851  |     |  1852  |  1853  |  1854  |  1855 

|  1856  |  1857  |  1858  |  1859  j     |  I860 

1861  |  1862  j  1863  |     |  18(54  |  1865  j  1866 

1867      |  1868  |  1869  |  1870  |  1871  ' 

1872  1873  1874  |  1875  |     |  1876  J  1877 

1878  )  1879  |     |  1880  |  1881  J  1882  j  1883 

|  1884  |  1885  |  18*6  |  1887  J     |  1888 

1889  |  1890  |  1891  j     j  1892  |  1893  |  1894 

1895  |     |  1896  j  1897  |  1898  j  1899  j  1900 

1901  |  190  J  1903  )     |  1904  |  1905  |  1906 

1907  |     j  1908  |  1909  |  1910  |  1911  | 

1912  |  1913  |  1914  j  1915  |     J  1916  |  1917 

1918  1919  |     |  1920  j  1921  j  1922  1923 

|  1924  |  1925  j  1926  j  1927  j     j  1928 

1929  j  1930  1  1931  |     |  1932  |  1933  |  1934 

1935  |     j  1936  |  1937  |  1938  J  1939  j 

1940  |  1941  |  1942  j  1943  |     |  1944  j  1945 

1946  |  1947  |     j  1948  |  1949  |  1950  j  1951 

1952  |  1953  |  1954  |  1955  |     |  1956 

October. 

Mo.  Tu.  |  We.  I  Th.  |  Fr.  |  Sat.  g. 

|  -7  |  14  |  21  |  28 

Tu.   We.  |  Th.  |  Fr.  |  Sat.  |  S.  1  Mo. 

1  |  8  |  15  |  22  |  29 

We.  Th.  |  Fr.   Sat.  |  <3J.  |  Mo.  j  Tu. 

•  2  |  9  |  16  |  23  1  30 

Th.   Fr.  |  Sat.  |  <=$.  |  Mo.  |  Tu.  |  We. 

3  |  10  |  17  |  24  |  31 

Fr.   Sat.   S.  1  Mo.  |  Tu.  |  We.  J  Th. 

4  |  11  1  18  |  25  | 

Sat.   g.  |  Mo.  |  Tu.  |  We.  |  Th.   Fr. 

5  1  12  |  19  |  26  | 

S.   Mo.  |  Tu.  |  We.  |  Th.  \  Fr.   Sat. 

6  1  13  |  20  |  27  | 

The  Year  and  Days  of  the  Week  for  both  Months  are  in  the  same  column. 

|  4  |  1  1  !  18  |  25 

Mo.   Tu.   We.  |  Th.  |  Fr.  |  Sat  IS. 

|  o  |  12  |  19  26 

Tu.   We.  |  Th.  |  Fr.   Sat.  |  g.  1  ^o. 

|  6  |  13  |  20  |  27 

We.  Th.  |  Fr.  |  Sat.  |  g.   Mo.   Tu. 

|  7  |  14  |  21  |  28 

Th.   Fr.  |  Sat.  |  g.  |  Mo.  |  Tu.  |  We. 

1  |  8  |  15  |  22  |  29 

Fr.   Sat.  |S.  |  Mo.  |  Tu.   We.  Th. 

2  |  9  |  16  j  23  |  30 

Sat.   S.  1  Mo.  |  Tu.  |  We.  |  Th.  |  Fr. 

3  |  10  1  17  |  24  | 

S.   Mo.  |  Tu.  |  We.  |  Th.   Fr,  |  Sat. 

November. 

1771      |  1772  |  1773  |  1774  |  1775  | 

• 

1776  |  1777  1778  1779  |      1780  |  1781 

1782  |  1783  |      1784  |  1785  |  1786  |  1787 

|  1788  |  1789  1790  |  1791  |     |  1792 

1793  |  1794  |  1795      |  1796  |  1797  |  1798 

1799  |  1800  |  1801  1802  |  1803  |     |  1804 

1805  |  1806  |  1807      |  1808  |  1809  |  1810 

1811  |      1812  1813  |  1814  |  1815  | 

1816  |  1817  1818  1819  |     |  1820  |  1821 

1822  |  1823       1824  |  1825  |  1826  |  1827 

|  1828  1829  1830  |  1831  |      1832 

1833  |  1834  1835      |  1*36  1837  |  1838 

1839  |      1840  1841  |  1842  1843  | 

1844  |  1845  |  1846  |  1847  |     |  1848  |  1849 

1850  |  1851  |     |  1852  |  1853  |  1854  1855 

|  1856  |  1857  |  1858  |  1859      |  1860 

1861  |  1862  |  1863  |     |  1864  |  1866  |  1866 

1867  |     |  1868  |  1869  |  1870  |  1871  | 

1872  1  1873  |  1874  |  1*75  |     |  1876  |  1877 

1878  |  1879  |     |  1880  |  1881  |  1882  |  1883 

|  1884  |  1885  |  18*6  |  1887      |  1888 

1889  |  1890  |  1891  |     |  1892  |  1893  |  1894 

1895  |     |  1896  |  1897  |  1898  |  1899  |  1900 

1901  |  1902  |  1903  |     |  1904  1905  |  1906 

1907  |     |  1908  |  1909  |  1910  1911  | 

1912  |  1913  |  1914  |  1915  |      1916  |  1917 

1918  |  1919  |     |  1920  |  1921  1922  |  1923 

|  1924  1925  |  1926  (  1927      |  192* 

1929  |  1930  [  1931  |      1932  |  1933  |  1934 

1935  |     [  1936  1  193?  1938  1  1939  1 

1940  |  1941  |  1942  |  1943      |  1944  |  1945 

1946  |  1947  |     |  1948  1949  |  1950  |  1951 

December. 

|  1952  |  1953  |  19o4  1955  |     '|  1956 

|  2  |  9  1  16  |  23  |  30 

Mo.  |  Tu.   We.  I  Th.   Fr.  |  Sat.  g. 

|  3  1  10  1  17  |  24  |  31 

Tu.   We.  Th.  |  Fr.   Sat.   g.   Mo. 

|  4  1  11  1  18  |  25  | 

We.  Th.   Fr.  |  Sat,   g.   Mo.   Tu. 

15  (12  |  19  12&| 

Th.   Fr.   Sat.  f  g.   Mo.  |  Tu.   We 

|  6)13  |  20  |27  | 

Fr.   Sat.   g.  f  Mo.   Tu.  |  We.   Th. 

|  7  1  14  |  21  |  28  | 

Sat.   g.   Mo.   Tu.   We.  Th.   Fr. 

I  |  8  1  15  |  22  |  29  | 

g.   Mo.   Tu.  |  We.  Th.  |  Fr.  |  Sat. 

The  Year  and  Days  of  the  Week  for  both  Months  are  in  the  same  column.  . 

N.  B  4|  Do  unto  me  as  you  would 
that  I  should  do  unto  you,"  PLtASE 
DO  NOT  LOAN  THIS  BOOK,  but 
give  my  address  to  yourfriends,  that 
they  may  do  as  you  have  done  :  "buy 
it."  W.  POWELL  WARE, 

Lock  Box  1929    P.  O.,  New  York. 


>     a/A 

FTHE        *A 

fERSlTY  J 


02534 


